Universal valued Abelian groups
نویسندگان
چکیده
منابع مشابه
Universal Abelian Groups
We examine the existence of universal elements in classes of infinite abelian groups. The main method is using group invariants which are defined relative to club guessing sequences. We prove, for example: Theorem: For n ≥ 2, there is a purely universal separable p-group in אn if, and only if, 20 ≤ אn. §0 Introduction In this paper “group” will always mean “infinite abelian group”, and “cardina...
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Let T be a torsion abelian group. We consider the class of all torsion-free abelian groups G satisfying Ext(G,T ) = 0 and search for λ-universal objects in this class. We show that for certain T there is no ω-universal group. However, for uncountable cardinals λ there is always a λ-universal group if we assume (V = L). Together with results by the second author this solves completely a problem ...
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Abstract. We prove that if μ < λ = cf(λ) < μ0 , then there is no universal reduced torsion free abelian group of cardinality λ. Similarly if א0 < λ < 20 . We also prove that if iω < μ < λ = cf(λ) < μ0 , then there is no universal reduced separable abelian p-group in λ. We also deal with the class of א1-free abelian group. (Note: both results fail if (a) λ = λ0 or if (b) λ is strong limit, cf(μ)...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2013
ISSN: 0001-8708
DOI: 10.1016/j.aim.2012.12.005